[10^2 means 10 squared]
1+4+5+5+6+9 = 3+2+3+7+8+7
Pair each digit on the left with one on the
right (for example 13,42,53,57,68,97).
The sum of these ix numbers will always equal
its mirror image.
13+42+53+57+68+97 = 79+86+75+35+24+31
Most remarkable, you can square every term in
these equations and they still hold good.
13^2+42^2+53^2+57^2+68^2+97^2 = 79^2+86^2+75^2+24^2+31^2
***
# 736 = 7 + 3^6
***
9 + 9 = 18; 9 × 9 = 81
24 + 3 = 27; 24 × 3 = 72
47 + 2 = 49; 47 × 2 = 94
497 + 2 = 499; 497 × 2 = 994
***
YOU KNOW THE SECRET NUMBER
For this trick, you will need a pencil and two pieces of paper. First write down your number on one of the sheets of paper. Fold your paper so that your friend can’t see it. Now give a sheet of paper to your friend. Tell him or her to think of a number and then write it down. But before he or she writes it down, tell him or her to have a three-digit number and have the largest number first then the smaller number and then the smallest number. For example: 742 or 971. Tell him not to let you see his number. Let’s pretend that the number is 861. Next tell him or her to turn the number around. The number would be 168. Now tell him or her to subtract the smallest number from the largest one. This would be 693. Now ask your partner to turn that number around and then the number would be 396. Now add them both together. This would be 1089. Now give him or her your paper and then watch his face when he sees that your number was 1089. The answer is always going to be 1089 so always write that number down.
Name the Number
You’ll need a pencil and a piece of paper. Give them to your friend and ask him to think of a number between 1 and 10. Then tell him or her to write their number on the sheet of paper. Have him or her put the paper where no one can see it! Let’s pretend your number is 6. You have to double it (12). Then tell him or her to add ten to the answer (22) and then divide that by two (11). Now tell your friend to yell out his or her final number (11). When he or her yells out their number all you have to do is subtract 5 (6). The trick will work every time. You have the simple job and your partner has the hard job. You can also use higher numbers than 10 such as 12 or 105.
Find the Dates
You will need two pieces of paper a pencil and another sheet of paper numbered from 1 to 31. Give the sheet of paper with numbers on it to your friend. Have him or her circle three numbers in a row. For example 17, 18, and 19. Now tell your friend to add the three numbers together. For example, 54. Tell him or her to write their answer down on a sheet of paper and give the piece of paper to you. All you have to do is divide the answer by 3. For example, 54 divided by 3 equals 18. The number you come out with will be the middle number. So now you add 1 to 18 (19) and subtract 1 from 18 (17). Now you can do this with any number.
.
With this trick you can tell someone their age the month that they were born in and the day they were born on. Now tell your friend to:
1) Write down the number of the month they were born on.
2) Multiply by 100.
3) Add the day of the month they were born on.
4) Multiply by 2.
5) Add 9.
6) Multiply by 5.
7) Add 8.
8) Multiply by 10.
9) Subtract 419.
10)Add his age.
11)Subtract 111.
The 2 digits on the right is the person’s age. The 2 digits on the left from the person’s age is the day that they were born on. The numbers that are left are the month your friend was born in.
Here is an example: Pretend that the person’s age is 16 and was born on November 4th.
1) He writes down 11 for November.
2) He multiplies by 100:1100
3) He adds the day of the month, 4:1104
4) He multiplies by 2:2208
5) He adds 9:2217
6) He multiplies by 5:11085
7) He adds 8: 11093
8) He multiplies by 10:110930
9) He subtracts 419:110511
10) He adds his age: 110527
11) Then he subtracts 111 and he gets 1110416.
The 2 numbers on the right tell you he is 16. The middle numbers tells you the day of the month he was born. The first 2 numbers tell you he was born in the 11th month, November.
******
Age and Address Please
Let’s suppose that someone is 31 years old and lives at 2979 Brunswick. Tell the person these instructions:
1) Write down their street number: 2979
2) Double it: 5958
3) Add 5: 5963
4) Multiply by 50: 298150
5) Add the person’s age (31): 2981181
6) Add the number of days in a year (365): 298546
The person tells you their result. You subtract 15 from the last two numbers and get the person’s age (46-15=31). You subtract 6 from the remaining number to get the person’s address (2985-6=2979).
Old Enough
Give a person these instructions:
1)Write down your age (actually you can just write down any number if you want).
2) Multiply it by 3.
3) Add 1 to the total
4) Multiply that by 3
5) Add the original number (your age)
Then you ask for the total. Suppose that someone writes down 23. They multiply it by 3 getting 69. The person adds 1 getting 70. It is multiplied by 3 equaling 210 and the original number is added which equals 233. When you are told this number you take away the last digit. This gives you 23, which is the original number.
Have a Roll
You will need 3 dice. Give the person 3 dice saying, “When my back is turned please roll these 3 dice.” Now tell the person these directions:
1) Multiply the number on die one by 2.
2) Add 5
3) Multiply by 5
4) Add the number from die 2 to the total
5) Multiply by 10
6) Add the number on die 3 to the total
Finally say, “What total did you get?” You subtract 250 from the number. Suppose the person tells you 612. 612-250=362. So the numbers showing on the dice are 3, 6, and 2.
******
A Palindromic recipe
A palindrome is usually a word (or sentence) which reads the same whether read forwards or backwards: for example "Madam, I'm Adam" (or her reply: "Eve").
We can also have palindromic numbers, such as 121, or 14641.
Here's a "recipe" for creating palindromic numbers:
Take any positive integer; reverse it (adding leading zeroes if necessary) and add this reversal to the original number. Repeat the operation using the result just obtained and eventually you will arrive at an answer which is palindromic.
Example (all numbers dozenal) :Start with 39
reverse it 93
add 110
reverse 011
add 121
121 is palindromic.
Start 293
reverse 392
add 665
reverse 566
add 100E
reverse E001
add 10010
reverse 01001
add 11011
11011 is palindromic
I've used base twelve, as usual, for my examples, but any base will do.
Now - is it always true? Will this method always produce a palindromic number from any starting number and in any base of numeration?
In bases four and five all numbers less than "1000" produce palindromes by this method. I haven't tried base six onwards yet.
If you like playing with numbers that should keep you busy for a while ...
Note: in base ten there are apparently thirteen numbers less than a thousand which do not produce a palindromic number even after thousands of steps. Will they eventually produce a palindrome? and how many steps will it take?
Anyone volunteering to find out which ones they are?
********
******************
6455 = (6^4 – 5) × 5
*****************
42263001 is a perfect square, and so is its reversal, 10036224.
******************
Square numbers containing all 10 digits unrepeated:
32043^2 = 1026753849
32286^2 = 1042385796
33144^2 = 1098524736
35172^2 = 1237069584
39147^2 = 1532487609
45624^2 = 2081549376
55446^2 = 3074258916
68763^2 = 4728350169
83919^2 = 7042398561
99066^2 = 9814072356
********
6455 = (6^4 – 5) × 5
*****
1x8+1=9
12x8+2=98
123x8+3=987
1234x8+4=9876
12345x8+5=98765
123456x8+6=987654
1234567x8+7=9876543
12345678x8+8=98765432
123456789x8+9=987654321
*****************
8^8 + 8^8 + 5^8 + 9^8 + 3^8 + 4^8 + 7^8 + 7^8 = 88593477
******************
Each of these (valid) equations uses the digits 1-9 exactly once:
42 × 138 = 5796
27 × 198 = 5346
39 × 186 = 7254
48 × 159 = 7632
28 × 157 = 4396
4 × 1738 = 6952
4 × 1963 = 7852
Even better: The numbers 3 and 51249876, between them, use all 9 digits — and so does their product, 153749628.
**********
,
MATHEMATICAL PALINDROMES
12X42=24X21
12X64=36X21
12X84=48X21
13X62=26X31
23X96=69X32
24X63=36X42
24X84=48X42
26X93=39X62
36X84=48X63
46X96=69X64
14X82=28X41
23X64=46X32
34X86=68X34
13X93=39X31
******
TEMPERATURE PALINDROME
16^0 Celsius = 61^0 Fahrenheit
28^0 Celsius = 62^0 Fahrenheit
***********
12 = 1
112 = 121
1112 = 12321
11112 = 1234321
111112 = 123454321
1111112 = 12345654321
11111112 = 1234567654321
111111112 = 123456787654321
1111111112 = 12345678987654321
******
MATHEMATICAL PUZZLE
123789+561945+642864 = 242868+323787+761943
Take away the central two numbers from each set and add
1289+5645+6464 = 2468+3287+7643
(13398) = (13398)
Take away the two central numbers from each set and add
19+55+64 = 28+37+73
(138) (138)
Most amazing: You can square every term above, in every
equation, and they all remain true.
********
12^2+33 = 1233
88^2=33 = 8833
588^2+2353^2 = 5882353
***********
********
12^2+33 = 1233
88^2=33 = 8833
588^2+2353^2 = 5882353
***********
A Mathematical Poem
A dozen, a gross, and a score,
Plus three times the square root of four,
Divided by seven,
Plus five times eleven,
Is nine squared and not a bit more.
- Leigh Mer
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